MATLAB: Using the bisection method, why is f(a) not a real integer or logical

bisection

I am trying to use the bisection method to optimize the cost of the pipeline, but I can't get a value for f(a)? What am I doing wrong with my while loop or if statement?
function [x] = myPipeBuilder(C_ocean, C_land, L, H)
%L=length of x, C_ocean=cost of pipeline in ocean, C_land=cost of pipeline on land, H=some distance in water
a=0;
b=L;
xM = (a + b)/2;
f(xM)= (C_ocean/sqrt(H^2+xM^2))-C_land;
% derivative of function
while abs(f(xM))>1*10^(-6)
% tolerance 
      if sign(f(a))==sign(f(xM))
          a=xM;
      elseif sign(f(b))==sign(f(xM))
          b=xM;
      end
      xM = (a + b)/2; 
end
x=xM;
end

Best Answer

You have the statement
f(xM)= (C_ocean/sqrt(H^2+xM^2))-C_land;
that does not define a function f(xM), it defines an assignment to the array elment f(xM) where xM would have to be a valid subscript. subscripts can only be non-negative integers. You calculated xM on the line above as xM = (a + b)/2; and we have no reason to expect that the result is going to be an integer. For example if L had been passed in as 19 then since b=L and a=0, then (a+b)/2 would be (0+19)/2 which would be 9.5 which would not be an integer.
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